Lecture 8. Digital Communications Part III. Digital Demodulation

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1 Lecure 8. Digial Communicaions Par III. Digial Demodulaion Binary Deecion M-ary Deecion Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

2 Analog Signal Source SOURCE A-D Conversion Digial Communicaions Bi sequence Digial Baseand Modulaion Digial Bandpass Modulaion Baseand Channel Bandpass Channel User D-A Conversion Digial Baseand Demodulaion Digial Bandpass Demodulaion Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

3 Digial Demodulaion 3 Bi sequence { } i Digial Baseand/Bandpass Modulaion Transmied Digial waveform Baseand/Bandpass Channel Bi sequence ˆ { } i Digial Baseand/Bandpass Demodulaion Corruped Digial waveform Wha are he sources of signal corrupion? How o deec he signal (o oain he i sequence { ˆ })? How o evaluae he fideliy performance? Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8 i

Sources of Signal Corrupion 4 4 Transmied signal s() Suppose ha channel andwidh is properly chosen such ha mos frequency componens of he ransmied signal can pass hrough he channel.

4 Sources of Signal Corrupion 4 4 Transmied signal s() Suppose ha channel andwidh is properly chosen such ha mos frequency componens of he ransmied signal can pass hrough he channel. Channel Thermal Noise: caused y he random moion of elecrons wihin elecronic devices. Received signal y() Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

5 Modeling of Thermal Noise 5 The hermal noise is modeled as a WSS process n(). The hermal noise is superimposed (added) o he signal: y()=s()+n() A each ime slo, n( ) (, ) (i.e., zero-mean Gaussian random variale wih variance ): f n ( ) ep a Pr{ X a} f ( d ) f ( y) dy Pr{ X a} a n n -a f n () a Pr{ X a} f ( d ) a n a Q Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

6 Modeling of Thermal Noise 6 The hermal noise has a power specrum ha is consan from dc o approimaely Hz: n() can e approimaely regarded as a whie process. N / Two-sided Power Specral Densiy N / The hermal noise is also referred o as addiive whie Gaussian Noise (AWGN), ecause i is modeled as a whie Gaussian WSS process which is added o he signal. Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

7 7 7 Deecion Transmied signal s() Received signal y()=s()+n() Sep : Filering Sep : Sampling Sep 3: Threshold Comparison Sample> Sample< Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

8 Bi Error Rae (BER) 8 Bi Error: { ˆ } { ˆ = u } { ˆ = u } i i i i i i Proailiy of Bi Error (or Bi Error Rae, BER): P Pr{ ˆ=, } Pr{ ˆ=, } i i i i Bi sequence { } i Digial Baseand/Bandpass Modulaion Transmied Digial waveform Baseand/Bandpass Channel Bi sequence ˆ { } i Digial Baseand/Bandpass Demodulaion Corruped Digial waveform Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

9 Digial Demodulaion 9 9 Corruped digial waveform y()=s()+n() Digial Baseand/Bandpass Demodulaion Bi sequence ˆ { } i Filer Sampler Threshold Comparison How o design he filer, sampler and hreshold o minimize he BER? Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

10 Binary Deecion Opimal Receiver Design BER of Binary Signaling Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

11 Binary Deecion Bi sequence { } i Binary Modulaion s () Transmied signal s ( i ) s( i ) if i if i Baseand/Bandpass Channel ˆ i if z ( ) ˆ i if z ( ) Threshold z( ) z() Comparison Sample a Filer h() Received signal y() s() n() BER: P Pr{ ˆ =, } Pr{ ˆ =, } i i i i How o choose he hreshold, sampling poin and he filer o minimize BER? Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

12 Receiver Srucure Transmied signal: s () s() if s() if Received signal y()=s()+n() Filer h() z() z( ) Threshold ˆ i if z ( ) Sample a Comparison ˆ i if z ( ) s() n() if Received signal: y () s () n () s() n() if Filer oupu: where so,() no() if z () so() no() so,() no() if oi, n ( ) n( ) h( ) d, o s () si( ) h( ) d, i,. n() is a whie process wih wo-sided power specral densiy N /. Is n o () a whie process? No! Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

13 Receiver Srucure 3 Transmied signal: s () s() if s() if Received signal y()=s()+n() Filer h() z() z( ) Threshold ˆ i if z ( ) Sample a Comparison ˆ i if z ( ) Received signal: s() n() if y () s () n () s() n() if Filer oupu: so,() no() if z () so() no() so,() no() if Sampler oupu: so,( ) no( ) if z ( ) so( ) no( ) so,( ) no( ) if ( ) (, z ( ) ( so,( ), ) no z ( ) ( s ( ), ) o, Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

14 BER 4 Received signal y()=s()+n() Filer h() z() z( ) Threshold ˆ i if z ( ) Sample a Comparison ˆ i if z ( ) BER: P Pr{ ˆ=, } Pr{ ˆ=, } Pr{ z ( ), } Pr{ z ( ), } Pr{ z ( ) }Pr{ } Pr{ z ( ) }Pr{ } Pr{ z ( ) } Pr{ z ( ) } (Pr{ } Pr{ } ) Recall ha z ( ) ( s ( ), ) and z ( ) ( s ( ), ) o, o, How o oain Pr{ z ( ) } and Pr{ z ( ) }? Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

15 5 BER Received signal y()=s()+n() Filer h() z() z( ) Sample a Threshold Comparison ˆ i ˆ i if z ( ) if z ( ) z ( ) ( s ( ), ) o, z ( ) ( s ( ), ) o, f ( z( ) ) Z f ( z( ) ) so,( ) so,( ) Z P is he area of he yellow zone! BER: P Pr{ z( ) } Pr{ z( ) } so,( ) so,( ) Q Q P is deermined y he hreshold Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

16 Opimal Threshold o Minimize BER 6 Received signal y()=s()+n() Filer h() z() z( ) Sample a Threshold Comparison ˆ i ˆ i if z ( ) if z ( ) Opimal hreshold o minimize BER: f ( z( ) ) Z f ( z( ) ) Z choose o minimize he yellow area! so,( ) so,( ) so,( ) so, ( ) f ( z( ) ) Z o, f ( z( ) ) Z s ( ) so,( ) Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

17 BER wih Opimal Threshold 7 Received signal y()=s()+n() Filer h() z() z( ) Sample a Threshold Comparison ˆ i ˆ i if if z ( ) z ( ) BER wih he opimal hreshold ( s ( ) ( )) o, so, is where so,( ) so,( ) so,( ) so,( ) P ( ) Q Q Q ( ( ) ( )) ( ) s s h d Q N h ( ) d s s s s h d ( ) ( ) ( ( ) ( )) ( ), o, o, and P ( ) is deermined y he filer h() and he sampling poin! N h ( ) d. Why? Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

18 Opimal Filer o Minimize BER 8 Received signal y()=s()+n() Filer h() z() z( ) Sample a Threshold Comparison ˆ i ˆ i if if z ( ) z ( ) Opimal filer o minimize P ( ) : min P ( ) ma h (), h (), h ( ) ks ( ( ) s( )), and ( s( ) s( )) h( ) d N h ( ) d ( s( ) s( )) h( ) d N h ( ) d ( s( ) s( )) d N / ( ( ) ( )) N h ( ) d s s d N / ( s ( ) s ( )) d h ( ) d = holds when = holds when h () ks ( ( ) s( )) Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

19 Mached Filer 9 Opimal filer: h () ks ( ( ) s( )) ( ) H( f) he ( ) j f d ( ( ) ( )) j f k s s e dks ( ( f) S( f)) e j f The opimal filer is called mached filer, as i has a shape mached o he shape of he inpu signal. Oupu of Mached Filer: Received signal y()=s()+n() Mached Filer h ( ) s( ) s( ) ( ) z() Sample a z( ) yh ( ) ( d ) y ()( s() s()) d Correlaion realizaion of Mached Filer: s() s() Inegraor z( ) Received signal y( )( s ( ) s( )) d y()=s()+n() X Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

20 Opimal Binary Deecor Mached Filer Received signal h ( ) s( ) s( ) y()=s()+n() ( ) Or equivalenly: s() s() Received signal y()=s()+n() X z() Sample a Inegraor z( ) y( )( s ( ) s ( )) d z( ) y( )( s ( ) s ( )) d ˆ i ˆ i if if z( ) z( ) Threshold Comparison ( E E ) o, o, ( E E ) Energy of s i (): E E s() d s() d ( s ( ) s ( )) ( s ( ) s ( )) h( ) d Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

21 BER of Opimal Binary Deecor ( ( ) ( )) ( ) s s h d - BER wih he opimal hreshold: P ( ) Q N h ( ) d - Impulse response of mached filer: h () s( ) s( ) ( ) - Opimal sampling poin: BER of he Opimal Binary Deecor: P ( ( ) ( ))( ( ) ( )) s s s s d Q N ( s ( ) s ( )) d ( s ( ) s( )) d Q N Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

22 Energy per Bi E and Energy Difference per Bi E d Energy per Bi: E ( E E ) ( s ( ) s ( )) d Energy difference per Bi: -E d can e furher wrien as d () () E s s d E s() d s() d s() s() d d ( ) E E s () s() d E Cross-correlaion coefficien is a measure of similariy eween wo signals s () and s (). Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

23 BER of Opimal Binary Deecor 3 BER of he Opimal Binary Deecor: P E d Q N E ( ) Q N The BER performance is deermined y ) E /N and ) Crosscorrelaion coefficien. P decreases as E /N increases. P is minimized when cross-correlaion coefficien =-. Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

24 4 BER of Binary Signaling Binary PAM, Binary OOK Binary ASK, Binary PSK, Binary FSK Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

25 BER of Binary PAM 5 Energy of s i (): E E A d A A Energy per i: E, BPAM EE A Cross-correlaion coefficien: ( ) -A s () s () BPAM E s () s () d A d E Power: BPAM A Opimal BER: P, BPAM E ( ) E Q Q N N A Q Q BPAM N R N, BPAM Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

26 BER of Binary OOK 6 Energy of s i (): E A, E. A Energy per i: EBOOK, ( EE) A Cross-correlaion coefficien: BOOK s () s() d E s () A s () Power: BOOK A / Opimal BER: P BOOK, E ( ) E Q Q N N A Q N BOOK Q R, BOOK N Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

27 Opimal Receivers of Binary PAM and OOK 7 Binary PAM: s () s () Received signal y() X Inegraor Threshold Comparison ( E E ) ˆ i ˆ i if if z( ) z( ) Binary OOK: Received signal y() X s () s () Inegraor Threshold Comparison A ˆ i ˆ if z( ) z( ) ( E E ) i if Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

28 BER of Binary ASK 8 Energy of s i (): E A, E. A Energy per i: Cross-correlaion coefficien: BASK s () s() d E E, BASK ( EE) 4 A s () Acos( fc) s () ( is an ineger numer of /f c ) Power: BASK A /4 Opimal BER: P, BASK E ( ) Q N E Q N A BASK Q Q 4N R N, BASK Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

29 BER of Binary PSK 9 Energy of s i (): Energy per i: Cross-correlaion coefficien: BPSK s () s () d s () d E E E A E, BPSK ( EE) A E A A s () Acos( f ) c s () Acos( f ) ( is an ineger numer of /f c ) s () s ( ) s () c Power: BPSK A / Opimal BER: P BPSK, E ( ) E Q Q N N A Q N Q BPSK R N, BPSK Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

30 Coheren Receivers of BASK and BPSK 3 BASK: Received signal y() s () s () X Inegraor Threshold Comparison ˆ i ˆ if z( ) E E i if ( ) 4 A z( ) BPSK: Received signal y() s () s () X Inegraor Threshold Comparison E E ( ) ˆ i ˆ i if if z( ) z( ) The opimal receiver is also called coheren receiver ecause i mus e capale of inernally producing a reference signal which is in eac phase and frequency synchronizaion wih he carrier signal cos( f ). Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8 c

31 Energy of s i (): Energy per i: Cross-correlaion coefficien: BER of Binary FSK E E A EBFSK, ( EE) A BFSK c c E cos(4 f) d cos(4 f ) c d cos(4 f) d 3 s () Acos( ( fc f)) s () Acos( ( fc f)) ( is an ineger numer of /( f f ) ) s () s () d cos( ( f f))cos( ( f f)) d Wha is he minimum f o achieve? min f A A BFSK R BFSK, 4 4 sin(4 f ) 4f Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8 c

32 Coheren BFSK Receiver 3 Power: BFSK A / Opimal BER: P BFSK, E ( ) E Q Q N N A BFSK Q Q N R, BFSK N cos( ( f f) ) c Received signal y()= s BFSK ()+n() z( ) ( E E ) f R BFSK, 4 cos( ( f f) ) c Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

33 Bandwidh Efficiency of Coheren BFSK 33 Wih f R BFSK, 4 : The required channel andwidh for 9% in-and power: B f R h _ 9%, BFSK.5R, BFSK Bandwidh efficiency of coheren BFSK: R BFSK, BFSK Bh _ 9%.4 Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

34 Summary I: Binary Modulaion and Demodulaion 34 Bandwidh Efficiency BER Binary PAM Binary OOK (9% in-and power) (9% in-and power) Q Q E BPAM, N E, BOOK N Coheren Binary ASK Coheren Binary PSK Coheren Binary FSK.5 (9% in-and power).5 (9% in-and power).4 (9% in-and power) Q Q Q E BASK, N E BPSK, N E BFSK, N Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

35 35 M-ary Deecion M-ary PAM M-ary PSK Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

36 Deecion of 4-ary PAM 36 Bi sequence { } i 4-ary PAM s ( i ) s( i ) s () s3( i ) s4( i ) Transmied signal i i i i i i i i Baseand Channel s () A, s (), A 3 s (), A 3 3 s () A, 4 ˆ ˆ ii ˆ ˆ ii ˆ ˆ ii ˆ ˆ i i if if if if z( ) z( ) z( ) 3 z( ) 3 Threshold Comparison z() Sample a z() Mached Filer Received signal y() s() n() Symol Error: { ˆ ˆ ii i i} { ˆ ˆ ˆ ˆ ii u i i } { i i u i i } { ˆ ˆ u } { ˆ ˆ u } i i i i i i i i Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

37 SER 37 Proailiy of Symol Error (or Symol Error Rae, SER): P Pr{ ˆ ˆ, } Pr{ ˆ ˆ, } s i i i i i i i i Pr{ ˆ ˆ, } Pr{ ˆ ˆ, } i i i i i i i i SER vs. BER: P Pr{ is received in error or is received in error} s i i Pr{ is received correcly and is received correcly} i i Pr{ is received correcly} Pr{ is received correcly} i i P P P for small ( P ) P Wha is he minimum SER of 4-ary PAM and how o achieve i? Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

38 Received signal y() SER: X s () s () Ps Pr{ z( ), i i } SER of 4-ary PAM Receiver 3 i i i i Threshold Comparison Pr{ z( ), i i } Pr{ z( ), i i } Pr{ z( ), } Pr{ z( ), } Pr{ z( ) 3, i i } Inegraor z( ) ˆ ˆ ii ˆ ˆ ii ˆ ˆ ii ˆ ˆ i i if if if if 38 z( ) z( ) z( ) 3 z( ) ( ˆ ˆ ii ) ( ˆ ˆ ii ) ( ˆ ˆ ii ) ( ˆ ˆ ) i i s() s() s() dn o( ) if i- i = z( ) (, ) i a i a s() s() s() dn ( ) o if i- i = z( ) (, ) i a i z( ) a s3() s() s() dn ( ) o if i- i = z( ) ( 3, ) i a i a 3 s4() s() s() dn ( ) o if i- i = z( ) ( 4, ) i a i a 4 Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8 3

39 Opimal Thresholds 39 f ( z( ) ) Z i i fz( z( ) i i ) fz( z( ) i i ) fz( z( ) i i ) SER a 4 a 3 a a a3 a4 a a3 a a 3 of he opimal 4-ary PAM receiver: Ps Pr{ z( ), i i } Pr{ z( ) 3, i i } Pr{ z( ), i i } Pr{ z( ), i i } Pr{ z( ) 3, i i } Pr{ z( ), i i } Pr z( ) ( a a ) Pr /4 ii 3 4 i i i i i i i i i i z a a i i Pr z( ) ( a3 a4) Pr z( ) ( a a3) Pr i i Pr z( ) ( a a3) Pr z( ) ( a a) Pr i i Pr ( ) ( ) Pr i i Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

40 SER of Opimal 4-ary PAM Receiver 4 fz( z( ) i i ) fz( z( ) i i ) fz( z( ) i i ) fz( z( ) i i ) a 4 a 3 a a a3 a4 a a3 a a 3 SER of he opimal 4-ary PAM receiver: P Pr z ( ) ( a a ) Pr z ( ) ( a a ) Pr z ( ) ( a a ) Pr z( ) ( 3) Pr ( ) ( ) Pr ( ) ( ) i a a z i i a a z i i a a i s 4 i i i i i i a3a 4 a a 3 a a Q Q Q 4 6 a a Q 4 a s () s () s () d i i N s () s () d P s 3 E d Q N Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

41 SER and BER of Opimal 4-ary PAM Receiver 4 SER: 3.4E s,4 PAM 3 E d,4pam 3.8E Ps,4PAM Q Q,4 PAM Q N N N BER: P P,4 PAM s,4pam 3 E,4 3 d PAM.8E,4PAM Q Q 4 N 4 N Energy difference E d : 4 E s s d s s d s s d d,4pam ( ( ) ( )) ( ( ) 3( )) ( 3( ) 4( )) Energy per symol E s : Es,4PAM s () d s () d s 3 () d s 4 () d Energy per i E : E E,4 PAM s,4pam 5 9 A 9 A Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8.8E S

42 Performance Comparison of Binary PAM and 4-ary PAM 4 BER (opimal receiver) Bandwidh Efficiency (9% in-and power) Binary PAM Q E, BPAM N 4-ary PAM 3.8,4 Q 4 N E PAM 4-ary PAM is more andwidh-efficien, u more suscepile o noise. Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

43 BER Comparison of Binary PAM and 4-ary PAM 43 Suppose E E E, BPAM,4PAM - 4-ary PAM P Binary PAM E / N ( db) Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

44 Binary PAM: Consellaion Represenaion of M-ary PAM -A A 4-ary PAM: -A -A/3 A/3 M-ary PAM: Energy per symol: M Es s () i d M d i Energy difference: -A () () E s s d d i d M ( A ( i) d) M 4A ( M ) d d A A d M A 3( M ) E S ( M )( M ) A ( A) M 44 s () A( i) d i i=,, M, Given E s, E d decreases as M increases! Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

45 SER of M-ary PAM 45 SER of M-ary PAM: P s ( M ) E d Q M N E d E M Es Elog M s P E s M N M d ( M ) 6E log M Q ( ) log M M E Given E, E d decreases as M increases; P s increases as M increases. A larger M leads o a smaller energy difference ---- a higher SER (As wo symols ecome closer in ampliude, disinguishing hem ecomes harder.) Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

46 Performance of M-ary PAM 46 Fideliy performance of M-ary PAM: P ( M ) 6E log M Q ( ) s M N M P s Bandwidh Efficiency of M-ary PAM: MPAM k log M (wih 9% in-and power) E / N ( db) Wih an increase of M, M-ary PAM ecomes: ) more andwidh-efficien; ) more suscepile o noise. Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

47 47 M-ary PSK Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

48 Coheren Demodulaor of QPSK A A QPSK sqpsk ( ) di cos( fc) dq sin( fc) 48 a cominaion of wo orhogonal BPSK signals d I if i if i d Q if i if i Coheren Demodulaor of QPSK Received signal y() s() n() cos( f ) c sin( f ) c z () z () ˆ ˆ i i Threshold Comparison if z( ) oherwise if z( ) oherwise ˆ i ˆ i Muliple ˆ { } i Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

49 BER of Coheren QPSK 49 BER of Coheren QPSK: P QPSK, E QPSK, Q N QPSK has he same BER performance as BPSK if E,QPSK =E,BPSK, u is more andwidh-efficien! Energy per i: E E QPSK, sqpsk, A 4 A R QPSK, Energy per symol: E s, QPSK A A R s, QPSK A R QPSK, Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

50 Performance Comparison of BPSK and QPSK 5 BER (coheren demodulaion) Bandwidh Efficiency (9% in-and power) Q BPSK E BPSK, N E, QPSK Q N QPSK.5 Wha if he wo signals, QPSK and BPSK, are ransmied wih he same ampliude A and he same i rae? Equally accurae! (BPSK requires a larger andwidh) Wha if he wo signals, QPSK and BPSK, are ransmied wih he same ampliude A and over he same channel andwidh? BPSK is more accurae! (u lower i rae) Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

51 M-ary PSK 5 M-ary PAM: ransmiing pulses wih M possile differen ampliudes, and allowing each pulse o represen log M is. -A A M-ary PSK: ransmiing pulses wih A M possile differen carrier phases, and allowing each pulse o represen log M is. A j( i ) si() Acos( fc i ) si () e i,..., M,. i=,, M-, M. Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

52 SER of M-ary PSK 5 s 4 () s 5 () s 36 () s 3 () s 7 () A s () () d s () s4 s8 () Wha is he minimum phase difference eween symols? /M Asin M Wha is he energy difference eween wo adjacen symols? Ed d A sin 4E S sin M M Wha is he SER wih opimal receiver? P s ES Q sin N M wih a large M Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

53 SER of M-ary PSK 53 E /N (db) A larger M leads o a smaller energy difference ---- a higher SER (As wo symols ecome closer in phase, disinguishing hem ecomes harder.) Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

54 Summary II: M-ary Modulaion and Demodulaion 54 Binary PAM 4-ary PAM M-ary PAM (M>4) Binary PSK QPSK M-ary PSK (M>4) Bandwidh Efficiency (9% in-and power) (9% in-and power) log M (9% in-and power).5 (9% in-and power) (9% in-and power) log M (9% in-and power) Q 3 Q 4 BER E BPAM,.8 N E,4 PAM N log 6log M E, Q MPAM M M N E, Q BPSK N E QPSK, Q N, Q sin log M log M M N Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8 E MPSK

55 Performance Comparison of Digial Modulaion Schemes R / B h The highes achievale andwidh efficiency : QPSK (SSB) 8PSK (SSB) E N 6PSK (SSB) 55 Required E /N when 5 : P BPSK: 9.6dB QPSK: 9.6dB 8PSK:.9dB 6PSK: 7.4dB -.6 / 5 BPSK 5 (SSB) E N ( db ) /4 Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

56 Digial Communicaion Sysems 56 { i } Digial Modulaion Transmied Digial waveform Channel Corruped Digial waveform Digial Demodulaion ˆ { } i Bandwidh Efficiency BER (Fideliy Performance) Informaion Bi Rae R Required Channel Bandwidh B h Binary: P E ( ) Q N Wha is he highes andwidh efficiency for given E /N? Informaion heory -- AWGN channel capaciy How o achieve he highes andwidh efficiency? Channel coding heory Wha if he channel is no an LTI sysem? Wireless communicaion heory Lin Dai (Ciy Universiy of Hong Kong) EE38 Principles of Communicaions Lecure 8

UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EECS 121 FINAL EXAM

UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EECS 121 FINAL EXAM Name: UNIVERSIY OF CALIFORNIA College of Engineering Deparmen of Elecrical Engineering and Compuer Sciences Professor David se EECS 121 FINAL EXAM 21 May 1997, 5:00-8:00 p.m. Please wrie answers on blank